Course materials for 2020-11-2 AFEC at XTBG.
Did you install picante and FD?
It’s better if you have those packages too.
Load pacakges.
## Illicium_macranthum Manglietia_insignis Michelia_floribunda
## Site1 1 0 0
## Site2 1 2 2
## Site3 1 0 0
## Site4 1 1 0
## Site5 1 0 0
## Beilschmiedia_robusta Neolitsea_chuii Lindera_thomsonii
## Site1 0 0 0
## Site2 2 0 0
## Site3 0 0 2
## Site4 0 0 2
## Site5 0 1 1
## Actinodaphne_forrestii Machilus_yunnanensis
## Site1 0 0
## Site2 0 0
## Site3 2 2
## Site4 2 0
## Site5 0 0
| Abbreviation | Trait | Unit |
|---|---|---|
| LMA | Leaf mass per area | g m-2 |
| LL | Leaf lifespans (longevity) | months |
| Amass | Maximum photosynthetic rates per unit mass | nnoml g-1 s-1 |
| Rmass | Dark resperation rates per unit mass | nnoml g-1 s-1 |
| Nmass | Leaf nitrogen per unit mass | % |
| Pmass | Leaf phosphorus per unit mass | % |
| WD | Wood density | g cm-3 |
| SM | Seed dry mass | mg |
trait_long <- trait %>%
gather(trait, val, 2:9)
ggplot(trait_long, aes(x = val)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")Probably we can do log-transformation for all the traits except for WD.
trait2 <- trait %>%
mutate(logLMA = log(LMA),
logLL = log(LL),
logAmass = log(Amass),
logRmass = log(Rmass),
logNmass = log(Nmass),
logPmass = log(Pmass),
logSM = log(SM)) %>%
dplyr::select(sp, logLMA, logLL, logAmass, logRmass, logNmass, logPmass, WD, logSM)
DT::datatable(trait2)trait2 %>%
gather(trait, val, 2:9) %>%
ggplot(., aes(x = val)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")Skip
## Run 0 stress 0
## Run 1 stress 9.744536e-05
## ... Procrustes: rmse 0.1288544 max resid 0.1986308
## Run 2 stress 9.489838e-05
## ... Procrustes: rmse 0.1288521 max resid 0.1986145
## Run 3 stress 7.044895e-05
## ... Procrustes: rmse 0.09291819 max resid 0.1402673
## Run 4 stress 8.23302e-05
## ... Procrustes: rmse 0.1288677 max resid 0.1986314
## Run 5 stress 0
## ... Procrustes: rmse 0.08145113 max resid 0.1100644
## Run 6 stress 0.2297529
## Run 7 stress 0
## ... Procrustes: rmse 0.07308683 max resid 0.1194549
## Run 8 stress 0.1302441
## Run 9 stress 0
## ... Procrustes: rmse 0.04192437 max resid 0.06171832
## Run 10 stress 0.2297529
## Run 11 stress 0
## ... Procrustes: rmse 0.1099842 max resid 0.1878721
## Run 12 stress 0
## ... Procrustes: rmse 0.06122222 max resid 0.09081168
## Run 13 stress 6.968383e-05
## ... Procrustes: rmse 0.1216506 max resid 0.182077
## Run 14 stress 0.09680973
## Run 15 stress 0
## ... Procrustes: rmse 0.05016184 max resid 0.0750991
## Run 16 stress 0.1302441
## Run 17 stress 0.2297529
## Run 18 stress 0.0968105
## Run 19 stress 7.031243e-05
## ... Procrustes: rmse 0.1289714 max resid 0.1987071
## Run 20 stress 6.946735e-05
## ... Procrustes: rmse 0.1430172 max resid 0.2603153
## *** No convergence -- monoMDS stopping criteria:
## 13: stress < smin
## 3: stress ratio > sratmax
## 4: scale factor of the gradient < sfgrmin
We can use the function ordiplot and orditorp to add text to the plot in place of points to make some more sence.
ordiplot(res_mds, type = "n")
orditorp(res_mds,display="species",col="red",air=0.01)
orditorp(res_mds,display="sites",cex=1.25,air=0.01)cophenetic() creates distance matrices based on phylogenetic trees. Let’s see the first 5 species.
## Acer_campbellii Melia_toosendan Skimmia_arborescens
## Acer_campbellii 0.0000000 0.18181818 0.18181818
## Melia_toosendan 0.1818182 0.00000000 0.09090909
## Skimmia_arborescens 0.1818182 0.09090909 0.00000000
## Rhus_sylvestris 0.3636364 0.36363636 0.36363636
## Sterculia_nobilis 0.5454545 0.54545455 0.54545455
## Rhus_sylvestris Sterculia_nobilis
## Acer_campbellii 0.3636364 0.5454545
## Melia_toosendan 0.3636364 0.5454545
## Skimmia_arborescens 0.3636364 0.5454545
## Rhus_sylvestris 0.0000000 0.5454545
## Sterculia_nobilis 0.5454545 0.0000000
\(MPD = \frac{1}{n} \Sigma^n_i \Sigma^n_j \delta_{i,j} \; i \neq j\), where \(\delta_{i, j}\) is the pairwised distance between species i and j
## [1] NA 1.568182 1.454545 1.606061 1.636364
The above vector shows MPD for each site.
\[ CWM_i = \frac{\sum_{j=1}^n a_{ij} \times t_{j}}{\sum_{j=1}^n a_{ij}} \]
## # A tibble: 8 x 9
## sp logLMA logLL logAmass logRmass logNmass logPmass WD logSM
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Actinodaphne_f… 4.24 2.53 5.01 2.17 0.412 -1.83 0.48 0.300
## 2 Beilschmiedia_… 3.61 3.09 5.72 3.53 1.75 -1.35 0.47 0.770
## 3 Illicium_macra… 5.66 4.75 3.27 0.793 -0.288 -3.51 0.4 -0.0305
## 4 Lindera_thomso… 4.47 3.70 5.49 3.02 0.626 -3.00 0.53 -0.734
## 5 Machilus_yunna… 4.26 3.36 4.65 2.69 0.239 -0.821 0.59 0.0770
## 6 Manglietia_ins… 6.22 5.24 3.10 0.255 -0.431 -3.91 0.45 -0.0513
## 7 Michelia_flori… 4.93 3.99 3.65 2.00 0.457 -3.91 0.54 0.621
## 8 Neolitsea_chuii 4.65 4.18 5.20 2.30 0.489 -2.12 0.43 -1.71
## Site1 Site2 Site3 Site4 Site5
## 1 7 7 6 3
## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 4.236712 2.527327 5.006359 2.173615 0.4121097 -1.832581 0.48
## Site2 31.729450 25.585161 33.973907 16.848875 4.5974297 -17.531309 3.28
## Site3 35.828159 29.342331 28.910240 11.266140 1.4425535 -21.721201 3.32
## Site4 30.140733 24.069613 24.233478 10.201674 2.2197972 -18.827747 2.93
## Site5 14.713415 11.128090 12.759265 5.116104 0.2203436 -6.565585 1.52
## logSM
## Site1 0.3001046
## Site2 0.3114643
## Site3 -1.9909259
## Site4 2.2087792
## Site5 0.3257723
## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 4.236712 2.527327 5.006359 2.173615 0.41210965 -1.832581 0.4800000
## Site2 4.532779 3.655023 4.853415 2.406982 0.65677568 -2.504473 0.4685714
## Site3 5.118308 4.191762 4.130034 1.609449 0.20607908 -3.103029 0.4742857
## Site4 5.023456 4.011602 4.038913 1.700279 0.36996620 -3.137958 0.4883333
## Site5 4.904472 3.709363 4.253088 1.705368 0.07344788 -2.188528 0.5066667
## logSM
## Site1 0.3001046
## Site2 0.0444949
## Site3 -0.2844180
## Site4 0.3681299
## Site5 0.1085908
We have a data.fame of traits. First we need to prepare a trait matrix, then a distance matrix based on trait values.
Let’s see a subset of the trait matrix
## logLMA logLL logAmass logRmass logNmass
## Acer_campbellii 3.684118 1.957274 6.892692 4.002047 1.8809906
## Actinodaphne_forrestii 4.236712 2.527327 5.006359 2.173615 0.4121097
## Alnus_nepalensis 4.743366 4.010419 4.341335 2.022871 0.5007753
## Anneslea_fragrans 4.190715 3.293241 5.162211 3.703522 1.4632554
## Beilschmiedia_robusta 3.614964 3.085573 5.722441 3.526655 1.7544037
Then, we will make trait distance matrix based on the Euclidean distance. There are other distance measures, for example Gower’s Distance, but we focus on the Euclidean distance today.
Before calulating distance, we need to make sure unit change in ditances have same for different traits. We will scale trait values so that then have mean = 0 and SD = 1. (e.g., \((X_i - \mu) / \sigma\))
trait_mat <- scale(trait_mat0)
par(mfrow = c(2, 2))
hist(trait_mat0[, "logLMA"])
hist(trait_mat[, "logLMA"])
hist(trait_mat0[, "WD"])
hist(trait_mat[, "WD"])Now we can make a trait distance matirx.
Let’s see the first 5 species.
## Acer_campbellii Actinodaphne_forrestii Alnus_nepalensis
## Acer_campbellii 0.000000 3.799360 5.216902
## Actinodaphne_forrestii 3.799360 0.000000 2.415031
## Alnus_nepalensis 5.216902 2.415031 0.000000
## Anneslea_fragrans 3.175911 2.335392 3.225141
## Beilschmiedia_robusta 2.545269 2.565063 3.638183
## Anneslea_fragrans Beilschmiedia_robusta
## Acer_campbellii 3.175911 2.545269
## Actinodaphne_forrestii 2.335392 2.565063
## Alnus_nepalensis 3.225141 3.638183
## Anneslea_fragrans 0.000000 1.579930
## Beilschmiedia_robusta 1.579930 0.000000
## [1] NA 4.288349 3.530805 3.961248 3.438008
## ntaxa mpd.obs mpd.rand.mean mpd.rand.sd mpd.obs.rank mpd.obs.z
## Site1 1 NA NaN NA NA NA
## Site2 4 4.288349 3.718044 0.7981511 761 0.7145337
## Site3 4 3.530805 3.737433 0.7862713 428 -0.2627945
## Site4 4 3.961248 3.711583 0.7912637 657 0.3155273
## Site5 3 3.438008 3.751037 0.9857789 420 -0.3175449
## mpd.obs.p runs
## Site1 NA 999
## Site2 0.761 999
## Site3 0.428 999
## Site4 0.657 999
## Site5 0.420 999
We will make a functional dendrogram using clustring methods. We use UPGMA in this example.
## FEVe: Could not be calculated for communities with <3 functionally singular species.
## FDis: Equals 0 in communities with only one functionally singular species.
## FRic: To respect s > t, FRic could not be calculated for communities with <3 functionally singular species.
## FRic: Dimensionality reduction was required. The last 5 PCoA axes (out of 7 in total) were removed.
## FRic: Quality of the reduced-space representation = 0.811349
## FDiv: Could not be calculated for communities with <3 functionally singular species.
## $nbsp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $sing.sp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $FRic
## Site1 Site2 Site3 Site4 Site5
## NA 5.453089 2.917904 3.000656 3.553247
##
## $qual.FRic
## [1] 0.811349
##
## $FEve
## Site1 Site2 Site3 Site4 Site5
## NA 0.7595456 0.6769400 0.7085376 0.7584941
##
## $FDiv
## Site1 Site2 Site3 Site4 Site5
## NA 0.7301943 0.7617251 0.9166699 0.8261683
##
## $FDis
## Site1 Site2 Site3 Site4 Site5
## 0.000000 2.710994 1.842262 2.311159 2.042416
##
## $RaoQ
## Site1 Site2 Site3 Site4 Site5
## 0.000000 8.376023 4.005094 5.664467 4.379844
##
## $CWM
## logLMA logLL logAmass logRmass logNmass logPmass
## Site1 1.4467783 1.17548950 -1.38976382 -1.9975087 -0.88119735 -1.2775781
## Site2 0.5666449 0.55085046 -0.56218769 -0.8908026 -0.09004842 -0.8660119
## Site3 -0.1410729 -0.33319385 0.27087040 -0.2062427 -0.24084641 0.2088166
## Site4 0.3670613 0.03104745 0.01551229 -0.7298853 -0.34295985 -0.5718506
## Site5 0.4305791 0.56352114 0.11718014 -0.5812855 -0.29128834 -0.6020974
## WD logSM
## Site1 -1.0150179 -0.2191496
## Site2 -0.2744691 0.1665816
## Site3 0.1242879 -0.2907346
## Site4 -0.2341187 -0.3397288
## Site5 -0.4833418 -0.9701997
## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.0.2 (2020-06-22)
## os Ubuntu 20.04 LTS
## system x86_64, linux-gnu
## ui X11
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Etc/UTC
## date 2020-11-01
##
## ─ Packages ───────────────────────────────────────────────────────────────────
## package * version date lib source
## abind 1.4-5 2016-07-21 [1] RSPM (R 4.0.0)
## ade4 * 1.7-15 2020-02-13 [1] RSPM (R 4.0.0)
## ape * 5.4-1 2020-08-13 [1] RSPM (R 4.0.2)
## assertthat 0.2.1 2019-03-21 [1] RSPM (R 4.0.0)
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## blob 1.2.1 2020-01-20 [1] RSPM (R 4.0.0)
## broom 0.7.0 2020-07-09 [1] RSPM (R 4.0.2)
## callr 3.4.3 2020-03-28 [1] RSPM (R 4.0.0)
## cellranger 1.1.0 2016-07-27 [1] RSPM (R 4.0.0)
## cli 2.0.2 2020-02-28 [1] RSPM (R 4.0.0)
## cluster 2.1.0 2019-06-19 [2] CRAN (R 4.0.2)
## colorspace 1.4-1 2019-03-18 [1] RSPM (R 4.0.0)
## crayon 1.3.4 2017-09-16 [1] RSPM (R 4.0.0)
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## DBI 1.1.0 2019-12-15 [1] RSPM (R 4.0.0)
## dbplyr 1.4.4 2020-05-27 [1] RSPM (R 4.0.0)
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## MASS 7.3-51.6 2020-04-26 [2] CRAN (R 4.0.2)
## Matrix 1.2-18 2019-11-27 [2] CRAN (R 4.0.2)
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## utf8 1.1.4 2018-05-24 [1] RSPM (R 4.0.0)
## vctrs 0.3.2 2020-07-15 [1] RSPM (R 4.0.2)
## vegan * 2.5-6 2019-09-01 [1] RSPM (R 4.0.0)
## withr 2.2.0 2020-04-20 [1] RSPM (R 4.0.0)
## xfun 0.15 2020-06-21 [1] RSPM (R 4.0.1)
## xml2 1.3.2 2020-04-23 [1] RSPM (R 4.0.0)
## yaml 2.2.1 2020-02-01 [1] RSPM (R 4.0.0)
##
## [1] /usr/local/lib/R/site-library
## [2] /usr/local/lib/R/library